Subgroups — C₂₃×#62609 #19210235

Order 5888.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3329	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3326	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3321	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3320	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3242	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3221	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3174	C₂	1	2	yes	maximal, complemented
20	C₂₃×#3171	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3137	C₂	1	2	yes	maximal, complemented
23	C₂₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#563	—	2	2	no	—
25	C₂₃×#562	—	2	2	no	—
26	C₂₃×#557	C₂²	1	1	yes	characteristic
27	C₂₃×#556	C₂²	1	1	yes	characteristic
28	C₂₃×#555	C₂²	1	1	yes	characteristic
29	C₂₃×#555	C₂²	1	2	yes	—
30	C₂₃×#554	—	2	1	no	—
31	C₂₃×#554	C₂²	1	1	yes	characteristic
32	C₂₃×#553	—	2	1	no	—
33	C₂₃×#553	C₂²	1	2	yes	—
34	C₂₃×#552	—	2	1	no	—
35	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
37	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₂₃×#548	—	2	1	no	—
39	C₂₃×#548	C₂²	1	2	yes	—
40	C₂₃×#547	C₂²	1	1	yes	characteristic
41	C₂₃×#547	C₂²	1	1	yes	characteristic
42	C₂₃×#544	—	2	1	no	—
43	C₂₃×#544	C₂²	1	2	yes	—
44	C₂₃×#542	—	2	2	no	—
45	C₂₃×#542	—	2	1	no	—
46	C₂₃×#541	C₂²	1	2	yes	—
47	C₂₃×#540	C₂²	1	2	yes	—
48	C₂₃×#539	—	2	2	no	—
49	C₂₃×#537	—	2	1	no	—
50	C₂₃×#536	—	2	1	no	—
51	C₂₃×#536	C₂²	1	2	yes	—
52	C₂₃×#533	C₂²	1	1	yes	characteristic
53	C₂₃×#532	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
55	C₂₃×#529	C₂²	1	1	yes	characteristic
56	C₂₃×#529	C₂²	1	1	yes	characteristic
57	C₂₃×#501	C₂²	1	1	yes	characteristic
58	C₂₃×#499	C₂²	1	2	yes	—
59	C₂₃×#496	C₂²	1	1	yes	characteristic
60	C₂₃×#492	C₂²	1	2	yes	—
61	C₂₃×#491	C₂²	1	2	yes	—
62	C₂₃×#491	C₂²	1	2	yes	—
63	C₂₃×#491	C₂²	1	2	yes	—
64	C₂₃×#490	C₂²	1	1	yes	characteristic
65	C₂₃×#489	C₂²	1	1	yes	characteristic
66	C₂₃×#489	C₂²	1	2	yes	—
67	C₂₃×#488	C₂²	1	2	yes	—
68	C₂₃×#488	C₂²	1	2	yes	—
69	C₂₃×#487	C₂²	1	2	yes	—
70	C₂₃×#487	C₂²	1	1	yes	characteristic
71	C₂₃×#487	C₂²	1	1	yes	characteristic
72	C₂₃×#487	C₂²	1	2	yes	—
73	C₂₃×#487	C₂²	1	1	yes	characteristic
74	C₂₃×#487	C₂²	1	1	yes	characteristic
75	C₂₃×#485	C₂²	1	2	yes	—
76	C₂₃×#485	C₂²	1	2	yes	—
77	C₂₃×#485	C₂²	1	2	yes	—
78	C₂₃×#484	C₂²	1	2	yes	—
79	C₂₃×#483	C₂²	1	2	yes	—
80	C₂₃×#482	C₂²	1	2	yes	—
81	C₂₃×#479	C₂²	1	2	yes	—
82	C₂₃×#479	C₂²	1	2	yes	—
83	C₂₃×#477	C₂²	1	1	yes	characteristic
84	C₂₃×#477	C₂²	1	2	yes	—
85	C₂₃×#476	C₂²	1	1	yes	characteristic
86	C₂₃×#475	C₂²	1	1	yes	characteristic
87	C₂₃×#475	C₂²	1	2	yes	—
88	C₂₃×#474	C₂²	1	1	yes	characteristic
89	C₂₃×#469	C₂²	1	1	yes	characteristic
90	C₂₃×#469	C₂²	1	1	yes	characteristic
91	C₂₃×#468	C₂²	1	1	yes	characteristic
92	C₂₃×#468	C₂²	1	1	yes	characteristic
93	C₂₃×#468	C₂²	1	2	yes	—
94	C₂₃×#468	C₂²	1	2	yes	—
95	C₂₃×#465	C₂²	1	2	yes	—
96	C₂₃×#465	C₂²	1	2	yes	—
97	C₂₃×#463	C₂²	1	2	yes	—
98	C₂₃×#463	C₂²	1	2	yes	—
99	C₂₃×#461	C₂²	1	1	yes	characteristic
100	C₂₃×#461	C₂²	1	1	yes	characteristic
101	C₂₃×#461	C₂²	1	1	yes	characteristic
102	C₂₃×#461	C₂²	1	1	yes	characteristic
103	C₂₃×#461	C₂²	1	2	yes	—
104	C₂₃×#461	C₂²	1	2	yes	—
105	C₂₃×#449	C₂²	1	2	yes	—
106	C₂₃×#449	C₂²	1	2	yes	—
107	C₂₃×#448	C₂²	1	2	yes	—
108	C₂₃×#448	C₂²	1	2	yes	—
109	C₂₃×#448	C₂²	1	2	yes	—
110	C₂₃×#448	C₂²	1	2	yes	—
111	C₂₃×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
113	C₂₃×#440	C₂²	1	2	yes	—
114	C₂₃×#440	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
119	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
121	C₂₃×#436	C₂²	1	2	yes	—
122	C₂₃×#436	C₂²	1	1	yes	characteristic
123	C₂₃×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
125	C₂₃×#433	C₂²	1	2	yes	—
126	C₂₃×#431	C₂²	1	1	yes	characteristic
127	C₂₃×#419	C₂²	1	2	yes	—
128	C₂₃×#419	C₂²	1	2	yes	—
129	C₂₃×#419	C₂²	1	2	yes	—
130	C₂₃×#417	C₂²	1	2	yes	—
131	C₂₃×#416	C₂²	1	2	yes	—
132	C₂×C₂₃×#103	C₂²	1	2	yes	—
133	C₂₃×#405	C₂²	1	2	yes	—
134	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	—	2	1	no	—
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₂₃	—	2	1	no	—
139	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
140	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
153	C₂₃×C₄⋊Q₈	—	2	1	no	—
154	C₂₃×C₄⋊Q₈	—	2	2	no	—
155	C₂₃×C₄⋊Q₈	—	2	2	no	—
156	C₂₃×C₄⋊Q₈	—	2	1	no	—
157	C₂₃×C₄⋊Q₈	—	2	1	no	—
158	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₂₃×#127	C₂³	1	1	yes	characteristic
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#126	—	2	1	no	—
172	C₂₃×#126	D₄	1	2	yes	—
173	C₂₃×#125	—	2	2	no	—
174	C₂₃×#125	—	2	1	no	—
175	C₂₃×#125	—	2	2	no	—
176	C₂₃×#125	—	2	2	no	—
177	C₂₃×#125	—	2	2	no	—
178	C₂₃×#125	D₄	1	1	yes	characteristic
179	C₂₃×#125	C₂³	1	2	yes	—
180	C₂₃×#125	C₂³	1	2	yes	—
181	C₂₃×#125	C₂³	1	1	yes	characteristic
182	C₂₃×#124	—	2	2	no	—
183	C₂₃×#124	—	2	2	no	—
184	C₂₃×#124	—	2	2	no	—
185	C₂₃×#124	—	2	2	no	—
186	C₂₃×#124	—	2	1	no	—
187	C₂₃×#124	D₄	1	1	yes	characteristic
188	C₂₃×#124	C₂³	1	2	yes	—
189	C₂₃×#124	C₂³	1	1	yes	characteristic
190	C₂₃×#123	—	2	1	no	—
191	C₂₃×#123	—	2	2	no	—
192	C₂₃×#123	—	2	2	no	—
193	C₂₃×#123	—	2	2	no	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	—	2	2	no	—
196	C₂₃×#123	—	2	2	no	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	D₄	1	2	yes	—
199	C₂₃×C₂²⋊Q₈	—	2	1	no	—
200	C₂₃×C₂²⋊Q₈	—	2	1	no	—
201	C₂₃×C₂²⋊Q₈	—	2	1	no	—
202	C₂₃×C₂²⋊Q₈	—	2	1	no	—
203	C₂₃×C₂²⋊Q₈	—	2	1	no	—
204	C₂₃×C₂²⋊Q₈	—	2	2	no	—
205	C₂₃×C₂²⋊Q₈	—	2	1	no	—
206	C₂₃×C₂²⋊Q₈	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	—	2	2	no	—
208	C₂₃×C₂²⋊Q₈	—	2	2	no	—
209	C₂₃×C₂²⋊Q₈	—	2	2	no	—
210	C₂₃×C₂²⋊Q₈	—	2	2	no	—
211	C₂₃×C₂²⋊Q₈	—	2	2	no	—
212	C₂₃×C₂²⋊Q₈	—	2	2	no	—
213	C₂₃×C₂²⋊Q₈	—	2	2	no	—
214	C₂₃×C₂²⋊Q₈	—	2	2	no	—
215	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
216	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂₃×#121	—	2	1	no	—
220	C₂₃×#121	—	2	1	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	—	2	2	no	—
223	C₂₃×#121	—	2	2	no	—
224	C₂₃×#121	—	2	1	no	—
225	C₂₃×#121	—	2	2	no	—
226	C₂₃×#121	—	2	2	no	—
227	C₂₃×#121	D₄	1	1	yes	characteristic
228	C₂₃×#121	C₂³	1	2	yes	—
229	C₂₃×#121	C₂³	1	1	yes	characteristic
230	C₂₃×#121	C₂³	1	1	yes	characteristic
231	C₂₃×#121	C₂³	1	2	yes	—
232	C₂₃×#121	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₂₃	—	2	1	no	—
234	C₄×Q₈×C₂₃	—	2	1	no	—
235	C₄×Q₈×C₂₃	—	2	1	no	—
236	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
237	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
238	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₂₃	—	2	2	no	—
241	C₄×D₄×C₂₃	—	2	1	no	—
242	C₄×D₄×C₂₃	—	2	1	no	—
243	C₄×D₄×C₂₃	—	2	2	no	—
244	C₄×D₄×C₂₃	—	2	2	no	—
245	C₄×D₄×C₂₃	—	2	1	no	—
246	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₂₃	C₂³	1	2	yes	—
249	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₂₃	C₂³	1	2	yes	—
251	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₂₃	C₂³	1	2	yes	—
253	C₂₃×#117	—	2	1	no	—
254	C₂₃×#117	—	2	2	no	—
255	C₂₃×#117	—	2	1	no	—
256	C₂₃×#117	—	2	1	no	—
257	C₂₃×#117	C₂³	1	2	yes	—
258	C₂₃×#117	C₂³	1	2	yes	—
259	C₂₃×#117	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
264	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
265	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
266	C₂₃×#107	C₂³	1	1	yes	characteristic
267	C₂₃×#107	C₂³	1	1	yes	characteristic
268	C₂₃×#107	C₂³	1	2	yes	—
269	C₂₃×#107	C₂³	1	2	yes	—
270	C₂₃×#106	C₂³	1	2	yes	—
271	C₂₃×#106	C₂³	1	2	yes	—
272	C₂₃×#106	C₂³	1	1	yes	characteristic
273	C₂₃×#106	C₂³	1	1	yes	characteristic
274	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
277	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₂₃×#103	C₂³	1	1	yes	characteristic
279	C₂₃×#103	C₂³	1	2	yes	—
280	C₂₃×#103	C₂³	1	2	yes	—
281	C₂₃×#103	C₂³	1	2	yes	—
282	C₂₃×#103	C₂³	1	2	yes	—
283	C₂₃×#103	C₂³	1	2	yes	—
284	C₂₃×#103	C₂³	1	2	yes	—
285	C₂₃×#103	C₂³	1	2	yes	—
286	C₂₃×#103	C₂³	1	1	yes	characteristic
287	C₂₃×#103	C₂³	1	2	yes	—
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	2	yes	—
290	C₂₃×#103	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	2	yes	—
293	C₂₃×#103	C₂³	1	2	yes	—
294	C₂₃×#102	C₂³	1	1	yes	characteristic
295	C₂₃×#102	C₂³	1	2	yes	—
296	C₂₃×#102	C₂³	1	1	yes	characteristic
297	C₂₃×#102	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	1	yes	characteristic
299	C₂₃×#102	C₂³	1	1	yes	characteristic
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×#97	C₂³	1	1	yes	characteristic
306	C₂₃×#97	C₂³	1	1	yes	characteristic
307	C₂₃×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	2	yes	—
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	#41×C₂₃	—	4	2	no	—
313	#41×C₂₃	—	4	2	no	—
314	#41×C₂₃	—	8	2	no	—
315	#41×C₂₃	—	8	2	no	—
316	C₂×Q₈×C₂₃	—	2	1	no	—
317	C₂×Q₈×C₂₃	—	2	1	no	—
318	C₂×Q₈×C₂₃	—	2	2	no	—
319	C₂×Q₈×C₂₃	—	2	2	no	—
320	C₂×Q₈×C₂₃	—	2	2	no	—
321	C₂×Q₈×C₂₃	—	2	1	no	—
322	C₂×Q₈×C₂₃	—	4	2	no	—
323	C₂×Q₈×C₂₃	—	4	2	no	—
324	C₂×Q₈×C₂₃	—	4	2	no	—
325	C₂×Q₈×C₂₃	—	4	2	no	—
326	C₂×Q₈×C₂₃	—	8	2	no	—
327	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
331	C₂×D₄×C₂₃	—	2	1	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	1	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	1	no	—
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	2	1	no	—
338	C₂×D₄×C₂₃	—	2	1	no	—
339	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₂₃	—	2	2	no	—
345	C₂²×C₄×C₂₃	—	2	2	no	—
346	C₂²×C₄×C₂₃	—	2	2	no	—
347	C₂²×C₄×C₂₃	—	2	1	no	—
348	C₂²×C₄×C₂₃	—	2	1	no	—
349	C₂²×C₄×C₂₃	—	2	1	no	—
350	C₂²×C₄×C₂₃	—	2	2	no	—
351	C₂²×C₄×C₂₃	—	2	2	no	—
352	C₂²×C₄×C₂₃	—	2	2	no	—
353	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
357	SD₁₆×C₂₃	—	4	2	no	—
358	SD₁₆×C₂₃	—	4	2	no	—
359	SD₁₆×C₂₃	—	4	1	no	—
360	SD₁₆×C₂₃	—	4	1	no	—
361	SD₁₆×C₂₃	—	4	2	no	—
362	SD₁₆×C₂₃	—	4	2	no	—
363	D₈×C₂₃	—	4	1	no	—
364	D₈×C₂₃	—	4	1	no	—
365	M₁₆×C₂₃	—	4	1	no	—
366	M₁₆×C₂₃	—	4	1	no	—
367	M₁₆×C₂₃	—	4	2	no	—
368	C₂×C₈×C₂₃	—	4	2	no	—
369	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
372	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
373	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₂₃	—	2	1	no	—
376	C₄⋊C₄×C₂₃	—	2	1	no	—
377	C₄⋊C₄×C₂₃	—	2	1	no	—
378	C₄⋊C₄×C₂₃	—	2	2	no	—
379	C₄⋊C₄×C₂₃	—	2	1	no	—
380	C₄⋊C₄×C₂₃	—	2	2	no	—
381	C₄⋊C₄×C₂₃	—	2	2	no	—
382	C₄⋊C₄×C₂₃	—	2	2	no	—
383	C₄⋊C₄×C₂₃	—	2	1	no	—
384	C₄⋊C₄×C₂₃	—	2	2	no	—
385	C₄⋊C₄×C₂₃	—	2	2	no	—
386	C₄⋊C₄×C₂₃	—	2	1	no	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	—	2	1	no	—
389	C₄⋊C₄×C₂₃	—	2	2	no	—
390	C₄⋊C₄×C₂₃	—	2	2	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	1	no	—
393	C₄⋊C₄×C₂₃	—	2	2	no	—
394	C₄⋊C₄×C₂₃	—	2	2	no	—
395	C₄⋊C₄×C₂₃	—	2	1	no	—
396	C₄⋊C₄×C₂₃	—	2	2	no	—
397	C₄⋊C₄×C₂₃	—	2	2	no	—
398	C₄⋊C₄×C₂₃	—	2	2	no	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₂₃	—	2	2	no	—
413	C₂²⋊C₄×C₂₃	—	2	2	no	—
414	C₂²⋊C₄×C₂₃	—	2	1	no	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	2	no	—
417	C₂²⋊C₄×C₂₃	—	2	1	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	1	no	—
420	C₂²⋊C₄×C₂₃	—	2	2	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	1	no	—
423	C₂²⋊C₄×C₂₃	—	2	1	no	—
424	C₂²⋊C₄×C₂₃	—	2	1	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	1	no	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	1	no	—
430	C₂²⋊C₄×C₂₃	—	2	1	no	—
431	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
436	C₄²×C₂₃	—	2	2	no	—
437	C₄²×C₂₃	—	2	2	no	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	—	2	2	no	—
440	C₄²×C₂₃	—	2	2	no	—
441	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
444	C₄²×C₂₃	C₂⁴	1	2	yes	—
445	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
446	#62609	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₂₃	—	2	1	no	—
448	C₂³×C₂₃	—	2	1	no	—
449	C₂³×C₂₃	—	2	1	no	—
450	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
451	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
452	Q₈×C₂₃	—	2	2	no	—
453	Q₈×C₂₃	—	2	2	no	—
454	Q₈×C₂₃	—	2	1	no	—
455	Q₈×C₂₃	—	2	1	no	—
456	Q₈×C₂₃	—	2	2	no	—
457	Q₈×C₂₃	—	2	2	no	—
458	Q₈×C₂₃	—	2	2	no	—
459	Q₈×C₂₃	—	4	2	no	—
460	Q₈×C₂₃	—	8	1	no	—
461	Q₈×C₂₃	—	8	2	no	—
462	Q₈×C₂₃	—	8	2	no	—
463	Q₈×C₂₃	—	8	2	no	—
464	Q₈×C₂₃	—	8	1	no	—
465	D₄×C₂₃	—	2	2	no	—
466	D₄×C₂₃	—	2	1	no	—
467	D₄×C₂₃	—	2	1	no	—
468	D₄×C₂₃	—	2	1	no	—
469	D₄×C₂₃	—	2	1	no	—
470	D₄×C₂₃	—	2	1	no	—
471	D₄×C₂₃	—	2	1	no	—
472	D₄×C₂₃	—	4	2	no	—
473	D₄×C₂₃	—	4	2	no	—
474	D₄×C₂₃	—	8	1	no	—
475	D₄×C₂₃	—	8	1	no	—
476	D₄×C₂₃	—	8	2	no	—
477	D₄×C₂₃	—	8	2	no	—
478	D₄×C₂₃	—	8	1	no	—
479	D₄×C₂₃	—	8	1	no	—
480	D₄×C₂₃	—	8	2	no	—
481	C₂×C₄×C₂₃	—	2	2	no	—
482	C₂×C₄×C₂₃	—	2	2	no	—
483	C₂×C₄×C₂₃	—	2	1	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	2	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	1	no	—
488	C₂×C₄×C₂₃	—	2	2	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	1	no	—
491	C₂×C₄×C₂₃	—	2	2	no	—
492	C₂×C₄×C₂₃	—	2	2	no	—
493	C₂×C₄×C₂₃	—	2	2	no	—
494	C₂×C₄×C₂₃	—	2	1	no	—
495	C₂×C₄×C₂₃	—	4	1	no	—
496	C₂×C₄×C₂₃	—	4	2	no	—
497	C₂×C₄×C₂₃	—	4	2	no	—
498	C₂×C₄×C₂₃	—	4	2	no	—
499	C₂×C₄×C₂₃	—	8	2	no	—
500	C₂×C₄×C₂₃	—	8	2	no	—
501	C₂×C₄×C₂₃	—	8	2	no	—
502	C₂×C₄×C₂₃	—	8	2	no	—
503	C₂×C₄×C₂₃	—	8	2	no	—
504	C₂×C₄×C₂₃	—	8	2	no	—
505	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
514	C₈×C₂₃	—	2	1	no	—
515	C₈×C₂₃	—	2	2	no	—
516	C₈×C₂₃	—	2	1	no	—
517	C₈×C₂₃	—	2	1	no	—
518	C₈×C₂₃	—	2	1	no	—
519	C₈×C₂₃	—	2	2	no	—
520	#3552	C₂×C₂₃	1	1	yes	characteristic, complemented
521	#3547	C₂×C₂₃	1	1	yes	characteristic, complemented
522	#3372	C₂×C₂₃	1	1	yes	characteristic, complemented
523	#3367	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#3360	C₂×C₂₃	1	1	yes	characteristic, complemented
525	#3359	C₂×C₂₃	1	1	yes	characteristic, complemented
526	#3330	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#3329	C₂×C₂₃	1	1	yes	characteristic, complemented
528	#3329	C₂×C₂₃	1	2	yes	complemented
529	#3326	C₂×C₂₃	1	2	yes	complemented
530	#3321	C₂×C₂₃	1	2	yes	complemented
531	#3320	C₂×C₂₃	1	2	yes	complemented
532	#3303	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#3298	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3242	C₂×C₂₃	1	2	yes	complemented
535	#3233	C₂×C₂₃	1	1	yes	characteristic, complemented
536	#3221	C₂×C₂₃	1	2	yes	complemented
537	#3206	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3174	C₂×C₂₃	1	2	yes	complemented
539	#3171	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3139	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3137	C₂×C₂₃	1	2	yes	complemented
542	#2969	C₂×C₂₃	1	1	yes	characteristic, complemented
543	C₂²×C₂₃	—	2	1	no	—
544	C₂²×C₂₃	—	2	2	no	—
545	C₂²×C₂₃	—	2	1	no	—
546	C₂²×C₂₃	—	2	2	no	—
547	C₂²×C₂₃	—	2	1	no	—
548	C₂²×C₂₃	—	2	2	no	—
549	C₂²×C₂₃	—	4	1	no	—
550	C₂²×C₂₃	—	4	1	no	—
551	C₂²×C₂₃	—	4	1	no	—
552	C₂²×C₂₃	—	4	1	no	—
553	C₂²×C₂₃	—	4	1	no	—
554	C₂²×C₂₃	—	4	1	no	—
555	C₂²×C₂₃	—	4	1	no	—
556	C₂²×C₂₃	—	4	1	no	—
557	C₂²×C₂₃	—	4	1	no	—
558	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
559	C₄×C₂₃	—	2	1	no	—
560	C₄×C₂₃	—	2	1	no	—
561	C₄×C₂₃	—	2	2	no	—
562	C₄×C₂₃	—	2	2	no	—
563	C₄×C₂₃	—	2	1	no	—
564	C₄×C₂₃	—	2	1	no	—
565	C₄×C₂₃	—	2	2	no	—
566	C₄×C₂₃	—	4	2	no	—
567	C₄×C₂₃	—	4	1	no	—
568	C₄×C₂₃	—	4	2	no	—
569	C₄×C₂₃	—	4	1	no	—
570	C₄×C₂₃	—	4	2	no	—
571	C₄×C₂₃	—	4	1	no	—
572	C₄×C₂₃	—	4	1	no	—
573	C₄×C₂₃	—	4	1	no	—
574	C₄×C₂₃	—	4	2	no	—
575	C₄×C₂₃	#577	1	2	yes	—
576	C₄×C₂₃	#585	1	1	yes	characteristic
577	C₄×C₂₃	#585	1	1	yes	characteristic
578	#563	—	2	2	no	—
579	#562	—	2	2	no	—
580	#557	C₂²×C₂₃	1	1	yes	characteristic
581	#556	C₂²×C₂₃	1	1	yes	characteristic
582	#555	C₂²×C₂₃	1	1	yes	characteristic
583	#555	C₂²×C₂₃	1	2	yes	—
584	#554	—	2	1	no	—
585	#554	C₂²×C₂₃	1	1	yes	characteristic
586	#553	—	2	1	no	—
587	#553	C₂²×C₂₃	1	2	yes	—
588	#552	—	2	1	no	—
589	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
590	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
591	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
592	#548	—	2	1	no	—
593	#548	C₂²×C₂₃	1	2	yes	—
594	#547	C₂²×C₂₃	1	1	yes	characteristic
595	#547	C₂²×C₂₃	1	1	yes	characteristic
596	#544	—	2	1	no	—
597	#544	C₂²×C₂₃	1	2	yes	—
598	#542	—	2	2	no	—
599	#542	—	2	1	no	—
600	#541	C₂²×C₂₃	1	2	yes	—
601	#540	C₂²×C₂₃	1	2	yes	—
602	#539	—	2	2	no	—
603	#537	—	2	1	no	—
604	#536	—	2	1	no	—
605	#536	C₂²×C₂₃	1	2	yes	—
606	#533	C₂²×C₂₃	1	1	yes	characteristic
607	#532	C₂²×C₂₃	1	1	yes	characteristic
608	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
609	#529	C₂²×C₂₃	1	1	yes	characteristic
610	#529	C₂²×C₂₃	1	1	yes	characteristic
611	#501	C₂²×C₂₃	1	1	yes	characteristic
612	#499	C₂²×C₂₃	1	2	yes	—
613	#496	C₂²×C₂₃	1	1	yes	characteristic
614	#492	C₂²×C₂₃	1	2	yes	—
615	#491	C₂²×C₂₃	1	2	yes	—
616	#491	C₂²×C₂₃	1	2	yes	—
617	#491	C₂²×C₂₃	1	2	yes	—
618	#490	C₂²×C₂₃	1	1	yes	characteristic
619	#489	C₂²×C₂₃	1	2	yes	—
620	#489	C₂²×C₂₃	1	1	yes	characteristic
621	#488	C₂²×C₂₃	1	2	yes	—
622	#488	C₂²×C₂₃	1	2	yes	—
623	#487	C₂²×C₂₃	1	2	yes	—
624	#487	C₂²×C₂₃	1	1	yes	characteristic
625	#487	C₂²×C₂₃	1	1	yes	characteristic
626	#487	C₂²×C₂₃	1	1	yes	characteristic
627	#487	C₂²×C₂₃	1	1	yes	characteristic
628	#487	C₂²×C₂₃	1	2	yes	—
629	#485	C₂²×C₂₃	1	2	yes	—
630	#485	C₂²×C₂₃	1	2	yes	—
631	#485	C₂²×C₂₃	1	2	yes	—
632	#484	C₂²×C₂₃	1	2	yes	—
633	#483	C₂²×C₂₃	1	2	yes	—
634	#482	C₂²×C₂₃	1	2	yes	—
635	#479	C₂²×C₂₃	1	2	yes	—
636	#479	C₂²×C₂₃	1	2	yes	—
637	#477	C₂²×C₂₃	1	2	yes	—
638	#477	C₂²×C₂₃	1	1	yes	characteristic
639	#476	C₂²×C₂₃	1	1	yes	characteristic
640	#475	C₂²×C₂₃	1	1	yes	characteristic
641	#475	C₂²×C₂₃	1	2	yes	—
642	#474	C₂²×C₂₃	1	1	yes	characteristic
643	#469	C₂²×C₂₃	1	1	yes	characteristic
644	#469	C₂²×C₂₃	1	1	yes	characteristic
645	#468	C₂²×C₂₃	1	1	yes	characteristic
646	#468	C₂²×C₂₃	1	2	yes	—
647	#468	C₂²×C₂₃	1	2	yes	—
648	#468	C₂²×C₂₃	1	1	yes	characteristic
649	#465	C₂²×C₂₃	1	2	yes	—
650	#465	C₂²×C₂₃	1	2	yes	—
651	#463	C₂²×C₂₃	1	2	yes	—
652	#463	C₂²×C₂₃	1	2	yes	—
653	#461	C₂²×C₂₃	1	1	yes	characteristic
654	#461	C₂²×C₂₃	1	2	yes	—
655	#461	C₂²×C₂₃	1	1	yes	characteristic
656	#461	C₂²×C₂₃	1	1	yes	characteristic
657	#461	C₂²×C₂₃	1	2	yes	—
658	#461	C₂²×C₂₃	1	1	yes	characteristic
659	#449	C₂²×C₂₃	1	2	yes	—
660	#449	C₂²×C₂₃	1	2	yes	—
661	#448	C₂²×C₂₃	1	2	yes	—
662	#448	C₂²×C₂₃	1	2	yes	—
663	#448	C₂²×C₂₃	1	2	yes	—
664	#448	C₂²×C₂₃	1	2	yes	—
665	#446	C₂²×C₂₃	1	1	yes	characteristic
666	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
667	#440	C₂²×C₂₃	1	2	yes	—
668	#440	C₂²×C₂₃	1	2	yes	—
669	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
671	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
672	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
673	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
674	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
675	#436	C₂²×C₂₃	1	1	yes	characteristic
676	#436	C₂²×C₂₃	1	2	yes	—
677	#435	C₂²×C₂₃	1	2	yes	—
678	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
679	#433	C₂²×C₂₃	1	2	yes	—
680	#431	C₂²×C₂₃	1	1	yes	characteristic
681	#419	C₂²×C₂₃	1	2	yes	—
682	#419	C₂²×C₂₃	1	2	yes	—
683	#419	C₂²×C₂₃	1	2	yes	—
684	#417	C₂²×C₂₃	1	2	yes	—
685	#416	C₂²×C₂₃	1	2	yes	—
686	C₂×#103	C₂²×C₂₃	1	2	yes	—
687	#405	C₂²×C₂₃	1	2	yes	—
688	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
689	C₂×C₂₃	—	4	1	no	—
690	C₂×C₂₃	—	4	2	no	—
691	C₂×C₂₃	—	8	1	no	—
692	C₂×C₂₃	—	8	1	no	—
693	C₂×C₂₃	—	8	1	no	—
694	C₂×C₂₃	#3500	1	1	yes	characteristic
695	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
696	C₂×C₂₃	#3586	1	1	yes	characteristic
697	C₂×#41	—	2	1	no	—
698	C₂×#41	—	2	1	no	—
699	C₂×#41	C₂³×C₂₃	1	2	yes	—
700	C₂²×Q₈	—	2	1	no	—
701	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
702	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
704	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
705	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
707	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
709	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
710	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
711	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
712	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
713	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
714	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
715	C₄⋊Q₈	—	2	2	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	2	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	—	2	1	no	—
720	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
721	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
724	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
728	#127	C₂³×C₂₃	1	1	yes	characteristic
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	1	no	—
734	#126	D₄×C₂₃	1	2	yes	—
735	#125	—	2	2	no	—
736	#125	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	—	2	2	no	—
740	#125	D₄×C₂₃	1	1	yes	characteristic
741	#125	C₂³×C₂₃	1	1	yes	characteristic
742	#125	C₂³×C₂₃	1	2	yes	—
743	#125	C₂³×C₂₃	1	2	yes	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	—	2	2	no	—
747	#124	—	2	2	no	—
748	#124	—	2	1	no	—
749	#124	D₄×C₂₃	1	1	yes	characteristic
750	#124	C₂³×C₂₃	1	1	yes	characteristic
751	#124	C₂³×C₂₃	1	2	yes	—
752	#123	—	2	1	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	D₄×C₂₃	1	2	yes	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
778	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
779	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
780	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	D₄×C₂₃	1	1	yes	characteristic
790	#121	C₂³×C₂₃	1	1	yes	characteristic
791	#121	C₂³×C₂₃	1	1	yes	characteristic
792	#121	C₂³×C₂₃	1	1	yes	characteristic
793	#121	C₂³×C₂₃	1	2	yes	—
794	#121	C₂³×C₂₃	1	2	yes	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
800	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
801	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₂₃	1	2	yes	—
812	C₄×D₄	C₂³×C₂₃	1	2	yes	—
813	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₂₃	1	2	yes	—
815	#117	—	2	1	no	—
816	#117	—	2	2	no	—
817	#117	—	2	1	no	—
818	#117	—	2	1	no	—
819	#117	C₂³×C₂₃	1	2	yes	—
820	#117	C₂³×C₂₃	1	2	yes	—
821	#117	C₂³×C₂₃	1	2	yes	—
822	C₂×C₄⋊C₄	—	2	1	no	—
823	C₂×C₄⋊C₄	—	2	1	no	—
824	C₂×C₄⋊C₄	—	2	1	no	—
825	C₂×C₄⋊C₄	—	2	1	no	—
826	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
827	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
828	#107	C₂³×C₂₃	1	1	yes	characteristic
829	#107	C₂³×C₂₃	1	1	yes	characteristic
830	#107	C₂³×C₂₃	1	2	yes	—
831	#107	C₂³×C₂₃	1	2	yes	—
832	#106	C₂³×C₂₃	1	2	yes	—
833	#106	C₂³×C₂₃	1	2	yes	—
834	#106	C₂³×C₂₃	1	1	yes	characteristic
835	#106	C₂³×C₂₃	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
839	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
840	#103	C₂³×C₂₃	1	1	yes	characteristic
841	#103	C₂³×C₂₃	1	2	yes	—
842	#103	C₂³×C₂₃	1	2	yes	—
843	#103	C₂³×C₂₃	1	2	yes	—
844	#103	C₂³×C₂₃	1	2	yes	—
845	#103	C₂³×C₂₃	1	2	yes	—
846	#103	C₂³×C₂₃	1	2	yes	—
847	#103	C₂³×C₂₃	1	2	yes	—
848	#103	C₂³×C₂₃	1	1	yes	characteristic
849	#103	C₂³×C₂₃	1	2	yes	—
850	#103	C₂³×C₂₃	1	2	yes	—
851	#103	C₂³×C₂₃	1	2	yes	—
852	#103	C₂³×C₂₃	1	2	yes	—
853	#103	C₂³×C₂₃	1	2	yes	—
854	#103	C₂³×C₂₃	1	2	yes	—
855	#103	C₂³×C₂₃	1	2	yes	—
856	#102	C₂³×C₂₃	1	1	yes	characteristic
857	#102	C₂³×C₂₃	1	2	yes	—
858	#102	C₂³×C₂₃	1	1	yes	characteristic
859	#102	C₂³×C₂₃	1	2	yes	—
860	#102	C₂³×C₂₃	1	1	yes	characteristic
861	#102	C₂³×C₂₃	1	1	yes	characteristic
862	#102	C₂³×C₂₃	1	1	yes	characteristic
863	#102	C₂³×C₂₃	1	1	yes	characteristic
864	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
867	#97	C₂³×C₂₃	1	1	yes	characteristic
868	#97	C₂³×C₂₃	1	1	yes	characteristic
869	#97	C₂³×C₂₃	1	2	yes	—
870	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₂₃	1	2	yes	—
873	C₄×C₈	C₂³×C₂₃	1	2	yes	—
874	C₂₃	#62609	1	1	yes	characteristic, direct product factor, Sylow
875	#41	—	4	2	no	—
876	#41	—	4	2	no	—
877	#41	—	8	2	no	—
878	#41	—	8	2	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	4	2	no	—
886	C₂×Q₈	—	4	2	no	—
887	C₂×Q₈	—	4	2	no	—
888	C₂×Q₈	—	4	2	no	—
889	C₂×Q₈	—	8	2	no	—
890	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
893	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
903	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
904	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
905	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
906	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
920	SD₁₆	—	4	2	no	—
921	SD₁₆	—	4	2	no	—
922	SD₁₆	—	4	1	no	—
923	SD₁₆	—	4	1	no	—
924	SD₁₆	—	4	2	no	—
925	SD₁₆	—	4	2	no	—
926	D₈	—	4	1	no	—
927	D₈	—	4	1	no	—
928	M₁₆	—	4	1	no	—
929	M₁₆	—	4	1	no	—
930	M₁₆	—	4	2	no	—
931	C₂×C₈	—	4	2	no	—
932	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
934	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
936	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
965	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
966	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
968	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
995	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1005	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₂₃	1	2	yes	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1013	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1014	Q₈	—	2	2	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	2	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	8	2	no	—
1023	Q₈	—	8	2	no	—
1024	Q₈	—	8	2	no	—
1025	Q₈	—	8	1	no	—
1026	Q₈	—	8	1	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	4	2	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	8	1	no	—
1037	D₄	—	8	1	no	—
1038	D₄	—	8	2	no	—
1039	D₄	—	8	1	no	—
1040	D₄	—	8	1	no	—
1041	D₄	—	8	2	no	—
1042	D₄	—	8	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	4	1	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1075	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1076	C₈	—	2	1	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₈	—	2	1	no	—
1081	C₈	—	2	2	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	C₂₃×#577	1	2	yes	—
1115	C₄	C₂₃×#585	1	1	yes	characteristic
1116	C₄	C₂₃×#585	1	1	yes	characteristic
1117	C₂	—	4	1	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	8	1	no	—
1120	C₂	—	8	1	no	—
1121	C₂	—	8	1	no	—
1122	C₂	C₂₃×#3500	1	1	yes	characteristic
1123	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1124	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#529 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3552	C₂	semidirect
2. C₂₃×#3547	C₂	semidirect
3. C₂₃×#3372	C₂	semidirect
4. C₂₃×#3367	C₂	semidirect
5. C₂₃×#3360	C₂	semidirect
6. C₂₃×#3359	C₂	semidirect
7. C₂₃×#3330	C₂	semidirect
8. C₂₃×#3329	C₂	semidirect
9. C₂₃×#3329	C₂	semidirect
10. C₂₃×#3326	C₂	semidirect
11. C₂₃×#3321	C₂	semidirect
12. C₂₃×#3320	C₂	semidirect
13. C₂₃×#3303	C₂	semidirect
14. C₂₃×#3298	C₂	semidirect
15. C₂₃×#3242	C₂	semidirect
16. C₂₃×#3233	C₂	semidirect
17. C₂₃×#3221	C₂	semidirect
18. C₂₃×#3206	C₂	semidirect
19. C₂₃×#3174	C₂	semidirect
20. C₂₃×#3171	C₂	semidirect
21. C₂₃×#3139	C₂	semidirect
22. C₂₃×#3137	C₂	semidirect
23. C₂₃×#2969	C₂	semidirect
446. #62609	C₂₃	direct (N × H)
520. #3552	C₂×C₂₃	semidirect
521. #3547	C₂×C₂₃	semidirect
522. #3372	C₂×C₂₃	semidirect
523. #3367	C₂×C₂₃	semidirect
524. #3360	C₂×C₂₃	semidirect
525. #3359	C₂×C₂₃	semidirect
526. #3330	C₂×C₂₃	semidirect
527. #3329	C₂×C₂₃	semidirect
528. #3329	C₂×C₂₃	semidirect
529. #3326	C₂×C₂₃	semidirect
530. #3321	C₂×C₂₃	semidirect
531. #3320	C₂×C₂₃	semidirect
532. #3303	C₂×C₂₃	semidirect
533. #3298	C₂×C₂₃	semidirect
534. #3242	C₂×C₂₃	semidirect
535. #3233	C₂×C₂₃	semidirect
536. #3221	C₂×C₂₃	semidirect
537. #3206	C₂×C₂₃	semidirect
538. #3174	C₂×C₂₃	semidirect
539. #3171	C₂×C₂₃	semidirect
540. #3139	C₂×C₂₃	semidirect
541. #3137	C₂×C₂₃	semidirect
542. #2969	C₂×C₂₃	semidirect
874. C₂₃	#62609	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3552	2
C₂₃×#3547	2
C₂₃×#3372	2
C₂₃×#3367	2
C₂₃×#3360	2
C₂₃×#3359	2
C₂₃×#3330	2
C₂₃×#3329	2
C₂₃×#3326	2
C₂₃×#3321	2
C₂₃×#3320	2
C₂₃×#3303	2
C₂₃×#3298	2
C₂₃×#3242	2
C₂₃×#3233	2
C₂₃×#3221	2
C₂₃×#3206	2
C₂₃×#3174	2
C₂₃×#3171	2
C₂₃×#3139	2
C₂₃×#3137	2
C₂₃×#2969	2
#62609	23

Subgroups — C23×#62609 #19210235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62609 #19210235